The theoretical foundations, methods, and algorithms developed to analyze the stability and postbuckling behavior of thin elastic axisymmetric shells are discussed. The algorithm for numerically studying the processes...
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The theoretical foundations, methods, and algorithms developed to analyze the stability and postbuckling behavior of thin elastic axisymmetric shells are discussed. The algorithm for numerically studying the processes of nonlinear deformation of thin-walled axisymmetric shells by the solution parametric continuation method is generalized to solving the practical problem of design of mechanical actuators of discrete action. The synthesis algorithm is based on the method of changing the subspace of control parameters, which is supplemented with the procedure of smooth transition in changing the subspaces. The efficiency of the proposed algorithm is illustrated by an example of synthesis of a thermobimetallic actuator of discrete action. The procedure of determining an isolated solution, whose existencewas predicted byV. I. Feodosiev, is considered in the framework of studying the process of nonlinear deformation of a corrugated membrane loaded by an external pressure.
We study the iterative algorithm proposed by Armstrong et al. (An iterative method for elliptic problems with rapidly oscillating coefficients, 2018. arXiv preprint arXiv:1803.03551) to solve elliptic equations in div...
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We study the iterative algorithm proposed by Armstrong et al. (An iterative method for elliptic problems with rapidly oscillating coefficients, 2018. arXiv preprint arXiv:1803.03551) to solve elliptic equations in divergence form with stochastic stationary coefficients. Such equations display rapidly oscillating coefficients and thus usually require very expensive numerical calculations, while this iterative method is comparatively easy to compute. In this article, we strengthen the estimate for the contraction factor achieved by one iteration of the algorithm. We obtain an estimate that holds uniformly over the initial function in the iteration, and which grows only logarithmically with the size of the domain.
An optimal control problem for a system involving an interval parameter is considered. The concepts of a universal optimal state and a universal optimal control are introduced. The existence and uniqueness of a univer...
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An optimal control problem for a system involving an interval parameter is considered. The concepts of a universal optimal state and a universal optimal control are introduced. The existence and uniqueness of a universal solution to the interval optimal control problem is proved, and an algorithm for its determination is presented. The interval optimal control problem for a system described by the boundary value problem for a second-order ordinary differential equation is solved as an example.
We describe algorithms for computing hyperbolic invariant sets of diffeomorphisms and their stable and unstable manifolds. This includes the calculation of Smale horseshoes and the stable and unstable manifolds of per...
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We describe algorithms for computing hyperbolic invariant sets of diffeomorphisms and their stable and unstable manifolds. This includes the calculation of Smale horseshoes and the stable and unstable manifolds of periodic points in any finite dimension.
An algorithm for the calculation of the electrostatic potential distribution governed by the Poisson-Boltzmann equation is presented. The algorithm is applicable to both a single planar surface and two parallel, ident...
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An algorithm for the calculation of the electrostatic potential distribution governed by the Poisson-Boltzmann equation is presented. The algorithm is applicable to both a single planar surface and two parallel, identical, planar surfaces. The surface under consideration is coated with an ion-penetrable membrane, which bears fixed charges. Both uniformly distributed fixed charges and nonuniformly distributed fixed charges due to the dissociation of the functional groups in the membrane are considered. The liquid phase contains an arbitrary a:b electrolyte or mixed a:b and c:d electrolytes. The result obtained for two parallel surfaces is readily applicable to the estimation of both the electrostatic pressure and the interaction free energy between these surfaces. (C) 1995 Academic Press, Inc.
A model of competitive innovation diffusion is considered. The model is based on the Lotka-Volterra system and an initial-boundary problem for a system of quasilinear parabolic equations. The maximum principle is prov...
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A model of competitive innovation diffusion is considered. The model is based on the Lotka-Volterra system and an initial-boundary problem for a system of quasilinear parabolic equations. The maximum principle is proved for the problem of diffusion of two competitive innovations, and sufficient conditions of existence of optimum control are obtained for the system. A numerical algorithm is constructed for solving optimum control problems, and numerical results for a model example are presented.
This paper proposes a kinematics methodology in twist coordinates for screw linkages. Based on the definition of a twist, both the angular velocity of a link and the linear velocity of a point on it may be explicitly ...
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This paper proposes a kinematics methodology in twist coordinates for screw linkages. Based on the definition of a twist, both the angular velocity of a link and the linear velocity of a point on it may be explicitly represented in twist coordinates. Through integration on the twist solution numerically or analytically, we may obtain the displacements. By differential or numerical differential interpolation of the twist, we can find the accelerations of the link. The most outstanding advantage of this kinematic algorithm is that only the numerical differential interpolation of the first order is required to calculate the acceleration while only the first order integration of the twist is enough to compute the displacement. This merit makes it particularly fit for developing programmes to accomplish the kinematics analysis of a spatial linkage.
The computational implementation of the algorithm for estimating the spectrum of Lyapunov exponents for systems of differential equations with delayed arguments is considered. Taking into account that for such systems...
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The computational implementation of the algorithm for estimating the spectrum of Lyapunov exponents for systems of differential equations with delayed arguments is considered. Taking into account that for such systems, as well as for boundary value problems, it is not possible to prove the well-known Oseledets theorem, which makes it possible to efficiently calculate the required values, we only have to talk about estimates of characteristic exponents, in a sense close to Lyapunov ones. In this paper, we propose two methods for processing solutions of systems linearized on an attractor, one of which is based on a set of impulse functions;the other one is based on a set of trigonometric functions. The flexibility of application of the indicated algorithms is demonstrated in the case of quasi-stable structures, when several Lyapunov exponents are close to zero. The developed methods are tested on the logistic equation with delay. The results illustrate the "closeness" of the estimated characteristics and Lyapunov exponents.
An inverse problem of bilayer textile thickness determination in dynamic heat and moisture transfer is presented satisfying the heat-moisture comfort level of human body. Heat and mass transfer law in bilayer textiles...
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An inverse problem of bilayer textile thickness determination in dynamic heat and moisture transfer is presented satisfying the heat-moisture comfort level of human body. Heat and mass transfer law in bilayer textiles is displayed by proving the existence and uniqueness of solution to the coupled partial differential equations with initial-boundary value conditions. The finite difference method is employed to derive the numerical solution to partial differential equations. The regularized solution of the inverse problem is reformulated into solving function minimum problem through the Tikhonov regularization method. The golden section method is applied to solve the direct search problem and achieve the optimal solution to the inverse problem. numerical algorithm and its numerical results provide theoretical explanation for textile materials research and development.
We revisit an earlier idea of Marcus and Pesce from 1987 for generating fields of values of by matrices via 2 by 2 matrix compressions and their easily constructed elliptical field of values. This approach is used to ...
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We revisit an earlier idea of Marcus and Pesce from 1987 for generating fields of values of by matrices via 2 by 2 matrix compressions and their easily constructed elliptical field of values. This approach is used to reduce the cost of finding the FOV boundary curve of a matrix and makes it more accurate at the same time. The new algorithm succeeds by using fewer eigenanalyses and constructing 2 by 2 matrix compression ellipses of for approximating instead of only eigenanalyses. An application to verify a counterexample to the Zemanek Conjecture for companion matrices of monic polynomials and their normalized derivatives in and , respectively, in dimension 4 is given.
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